A101934 Numbers n with omega(n) smaller than omega(n-1) and omega(n+1).

11, 13, 19, 23, 25, 27, 29, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 131, 137, 139, 149, 151, 155, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227

Offset: 1

Author

Neil Fernandez, Dec 21 2004

Keywords

• easy
• nonn

Examples

			125 is in the sequence because it has one unique prime factor (5), which is fewer than its neighbors 124 (two such factors, namely 2 and 31) and 126 (two such factors, namely 2 and 53).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A101932, A076763.

Programs

Mathematica

For[i=2, i<1000, If[And[Length[FactorInteger[i 1]]>Length[FactorInteger[i]], Length[FactorInteger[i+1]] > Length[FactorInteger[i]]], Print[i]];i++ ]
(* Second program: *)
Select[Range[1000], PrimeNu[#] < Min[PrimeNu[#-1], PrimeNu[#+1]]&] (* Jean-François Alcover, Nov 14 2016 *)
Flatten[Position[Partition[PrimeNu[Range[250]],3,1],?(#[[1]]>#[[2]]<#[[3]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Apr 18 2021 *)